Lyapunov stable chain recurrence classes for singular flows

2022/02/20 by Shaobo Gan, Jiagang Yang, Gan, Shaobo +3
Mathematics · Physics and Astronomy · #37C10 #37C27 #37C29 #37D30 #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2202.09742

openalex publication_date 2022/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for a C¹ generic vector field X away from homoclinic tangencies, a nontrivial Lyapunov stable chain recurrence class is a homoclinic class. The proof uses an argument with C² vector fields approaching X in C¹ topology, with their Gibbs F-states converging to a Gibbs F-state of X.

Related

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